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Directed acyclic graphs (DAGs) encode a lot of information about a particular distribution in their structure. However, compute required to infer these structures is typically super-exponential in the number of variables, as inference…
The paper deals with two issues: the existence of universal models of a theory T and related properties when cardinal arithmetic does not give this existence offhand. In the first section we prove that simple theories (e.g., theories…
In this paper, we consider the Visibility Graph Recognition and Reconstruction problems in the context of terrains. Here, we are given a graph $G$ with labeled vertices $v_0, v_1, \ldots, v_{n-1}$ such that the labeling corresponds with a…
The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are $\epsilon$-far from satisfying the property. There are now several general results in this area which show that natural…
We study a graph-theoretic property known as robustness, which plays a key role in certain classes of dynamics on networks (such as resilient consensus, contagion and bootstrap percolation). This property is stronger than other graph…
An {\em ordered $r$-graph} is an $r$-uniform hypergraph whose vertex set is linearly ordered. Given $2\leq k\leq r$, an ordered $r$-graph $H$ is {\em interval} $k$-{\em partite} if there exist at least $k$ disjoint intervals in the ordering…
A graph property P is strongly testable if for every fixed \epsilon>0 there is a one-sided \epsilon-tester for P whose query complexity is bounded by a function of \epsilon. In classifying the strongly testable graph properties, the first…
Graph convolutional neural networks (GCNNs) have become a machine learning workhorse for screening the chemical space of crystalline materials in fields such as catalysis and energy storage, by predicting properties from structures.…
We present a unified pipeline for univariate time series classification via complex networks and persistent homology. A time series is mapped to a graph through one of five constructions across three families (visibility (natural and…
This paper explores the information-theoretic limitations of graph property testing in zero-field Ising models. Instead of learning the entire graph structure, sometimes testing a basic graph property such as connectivity, cycle presence or…
Artificial objects usually have very stable shape features, which are stable, persistent properties in geometry. They can provide evidence for object recognition. Shape features are more stable and more distinguishing than appearance…
We consider an edge-weighted uniform random graph with a given degree sequence (Repeated Configuration Model) which is a useful approximation for many real-world networks. It has been observed that the vertices which are separated from the…
For a first-order formula $\phi(x;y)$ we introduce and study the characteristic sequence $<P_n : n < \omega>$ of hypergraphs defined by $P_n(y_1,...,y_n) := (\exists x) \bigwedge_{i \leq n} \phi(x;y_i)$. We show that combinatorial and…
Order types are a well known abstraction of combinatorial properties of a point set. By Mn\"ev's universality theorem for each semi-algebraic set $V$ there is an order type with a realization space that is \emph{stably equivalent} to $V$.…
While routinely used in other areas of dynamics, image sets are ill-defined objects in general non-invertible measurable dynamics. We propose a way of consistently working with image sets of null-preserving (and hence, in particular, of…
Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
Recent works of Alon-Shapira and R\"odl-Schacht have demonstrated that every hereditary property of undirected graphs or hypergraphs is testable with one-sided error; informally, this means that if a graph or hypergraph satisfies that…
Given a `genus' function $g=g(n)$, we let $\mathcal{E}^g$ be the class of all graphs $G$ such that if $G$ has order $n$ (that is, has $n$ vertices) then it is embeddable in a surface of Euler genus at most $g(n)$. Let the random graph $R_n$…
A graph property P is said to be testable if one can check if a graph is close or far from satisfying P using few random local inspections. Property P is said to be non-deterministically testable if one can supply a "certificate" to the…